Question

number 6
\frac{75x^{3}y^{6}}{3x^{2}y^{2}}

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 75 by 3: $\frac{75}{3} = 25$.

Step2: Simplify the \(x\)-term

Use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$. For \(x\)-terms: $\frac{x^3}{x^2}=x^{3 - 2}=x^1 = x$.

Step3: Simplify the \(y\)-term

Use the rule of exponents $\frac{y^m}{y^n}=y^{m - n}$. For \(y\)-terms: $\frac{y^6}{y^2}=y^{6 - 2}=y^4$.

Step4: Combine the results

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together: $25\times x\times y^4 = 25xy^4$.

Answer:

\(25xy^4\)